
The accreting gas absorbs the line-integrated flux with 0.5 mag or more only for accretion rates \(\dot{M} \gtrsim 3\times 10^{-5}~M_{\mathrm {J}}\,\mathrm {yr}^{-1}\) 
in spherical symmetry (SpherAcc)
or \(\dot{M} \gtrsim 3\times 10^{-6}~M_{\mathrm {J}}\,\mathrm {yr}^{-1}\)  for polar accretion,
with a weak mass dependence (Figure REF ).
In the MagAcc case the mass dependence is stronger.
Except for MagAcc-Cold, the amount of extinction increases towards smaller masses.
This is partly due to the increase in density with decreasing planet mass at a given \(\dot{M}\)  (see Equation (REF )). Another reason is that the opacity happens mostly to increase with decreasing mass (see Figure REF ).
Up to \(\dot{M} \approx 3\times 10^{-4}~M_{\mathrm {J}}\,\mathrm {yr}^{-1}\)  and for masses above \(M_{\mathrm {p}}=10~M_{\mathrm {J}}\) , the gas absorbs with at most \(A_{\mathrm {H}\,\alpha } \lesssim 4\)  mag in the SpherAcc and Polar geometries.

At low \(\dot{M}\) , the observed line profile is the same as the one leaving the planet, but moderate to high \(\dot{M} \)  values lead to clear spectral features. There is no systematic trend in these features because they are due to several molecular and atomic lines. Larger amounts of extinction tend to be associated with a “spiky” spectrum showing features visible at a resolution of 10–20 \(\mathrm {km}\,\mathrm {s^{-1}}\)  (\(R\gtrsim 15,000\) ; Figure REF ) and suggest relatively localised absorption, as could occur in a magnetospheric accretion geometry.

Larger-scale (\(\Delta v\sim 100~\mathrm {km}\,\mathrm {s^{-1}}\) ) slopes in the gas opacity at H \(\alpha \)  introduce asymmetries in the line shape. This is often
more important than
asymmetries in the line emerging from the shock.

Based on the recent literature, we estimated that the accreting dust has an extinction curve shallower than in the ISM [1]}, [2]}.
A conservative range of opacity values at H \(\alpha \)  is
\(\kappa _{\mathrm {dust,\,H}\,\alpha }\sim 10^{-2}\) –10 cm\(^2\)  g\(^{-1}_{\textrm {gas}}\)  at \(f_{\textrm {d/g}}\sim 10^{-5}\) –\(3\times 10^{-4}\)  (Figure REF ),
which is 10–\(10^4\)  times lower than in the ISM.
Our dust opacity implies that for most parameter combinations the absorption by the dust is negligible to small (Section REF ).

For a given planet mass there is a maximal H \(\alpha \)  luminosity because absorption increases more strongly with \(\dot{M} \)  than \({L_{\textnormal {H}\,\alpha }} \)  does (Figure REF ). Considering only the gas opacity, this maximum is \({L_{\textnormal {H}\,\alpha }} \approx 10^{-4}~{L_\odot }\)  for \(M_{\mathrm {p}}\sim 10~M_{\mathrm {J}}\) . Lower masses peak at lower \({L_{\textnormal {H}\,\alpha }}\) .
Therefore, for certain values,
an \({L_{\textnormal {H}\,\alpha }}\)  measurement can be interpreted as two different accretion rates, a low or a high value.
Also considering some dust absorption implies \(\dot{M}\)  values between the two extremes.

The current computational capacities impose a coarse spatial resolution of the flow near the planet in multidimensional studies. This affects dramatically their estimate of the flow's contribution to the absorption (Section REF ). This highlights the complementarity of our approach, which assumes a simplified geometry but more realistic densities, temperatures, and velocities in the accretion flow and at the shock.

The accretion rate onto Delorme 1 (AB)b is much too low for absorption by gas or dust in the accretion flow to matter (Section REF ).
For PDS 70 b, we used the indication of a low mass and the observed luminosity to derive from our models a range of possible accretion rates and extinctions. We found \(10^{-7} \lesssim (\dot{M}/M_{\mathrm {J}}\,\mathrm {yr}^{-1}) \lesssim 10^{-4}\)  and \(A_{\mathrm {H}\,\alpha } \lesssim 4\)  mag (\(A_V\lesssim 5\)  mag).

